One worry is that that piece of wood is likely a veneered ply.
Heavy sanding is not possible in that case.
did water get in behind that panel?
The stains look to be about the height where objects on the nav table
could chafe it.
Have you tried all the conventional cleaners?
Oxalyic acid (Barkeeper's Friend) is in the one part teak cleaners sold at WM.
It may remove lighten up some of the stains.
Light sanding with a fine grit (#220 or higher), re-oil and/or varnish
and hope for the best.

This isn't my boat, just one I'm considering, so I haven't tried removing this stain yet. The chain plate above leaked at one time, and dripped down the back of the wood in the photo. It is a veneer over ply.

It's a bit of a project but completely do able. Strip the varnish off, bleach the wood, seal the wood and re varnish. I have done it in my boat and it looks brand new. Of course, I am assuming that the wood behind it is solid and not rotted.

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